Overture Technical Report Series No. TR-001 May 2020 VDM-10 Language Manual by Peter Gorm Larsen Kenneth Lausdahl Nick Battle John Fitzgerald Sune Wolff Shin Sahara Marcel Verhoef Peter W. V. Tran-Jørgensen Tomohiro Oda Paul Chisholm Overture – Open-source Tools for Formal Modelling VDM-10 Language Manual Document history Month Year Version Version of Overture.exe Comment April 2010 0.2 May 2010 1 0.2 February 2011 2 1.0.0 July 2012 3 1.2.2 April 2013 4 2.0.0 March 2014 5 2.0.4 Includes RMs #16, #17, #18, #20 November 2014 6 2.1.2 Includes RMs #25, #26, #29 August 2015 7 2.3.0 Includes RMs #27 April 2016 8 2.3.4 Review inputs from Paul Chisholm September 2016 9 2.4.0 RMs #35, #36 May 2017 10 2.5.0 RM #39 Feb 2018 11 2.6.0 Includes RM #42 May 2020 12 2.7.4 Includes RM #44,#47,#48 ii Contents 1 Introduction 1 1.1 The VDM Specification Language (VDM-SL) . .1 1.2 The VDM++ Language . .1 1.3 The VDM Real Time Language (VDM-RT) . .2 1.4 Purpose of The Document . .2 1.5 Structure of the Document . .2 2 Concrete Syntax Notation 3 3 Data Type Definitions 5 3.1 Basic Data Types . .5 3.1.1 The Boolean Type . .6 3.1.2 The Numeric Types . .8 3.1.3 The Character Type . 11 3.1.4 The Quote Type . 11 3.1.5 The Token Type . 12 3.2 Compound Types . 12 3.2.1 Set Types . 13 3.2.2 Sequence Types . 15 3.2.3 Map Types . 18 3.2.4 Product Types . 22 3.2.5 Composite Types . 23 3.2.6 Union and Optional Types . 26 3.2.7 The Object Reference Type (VDM++ and VDM-RT) . 28 3.2.8 Function Types . 29 3.3 Invariants . 31 3.4 Equality . 32 3.5 Order . 35 4 Algorithm Definitions 39 iii VDM-10 Language Manual 5 Function Definitions 41 5.1 Polymorphic Functions . 47 5.2 Higher Order Functions . 49 6 Expressions 51 6.1 Let Expressions . 51 6.2 The Define Expression . 54 6.3 Unary and Binary Expressions . 55 6.4 Conditional Expressions . 56 6.5 Quantified Expressions . 58 6.6 The Iota Expression . 60 6.7 Set Expressions . 61 6.8 Sequence Expressions . 63 6.9 Map Expressions . 65 6.10 Tuple Constructor Expressions . 66 6.11 Record Expressions . 66 6.12 Apply Expressions . 68 6.13 The New Expression (VDM++ and VDM-RT) . 69 6.14 The Self Expression (VDM++ and VDM-RT) . 70 6.15 The Threadid Expression (VDM++ and VDM-RT) . 71 6.16 The Lambda Expression . 72 6.17 Narrow Expressions . 73 6.18 Is Expressions . 76 6.19 Base Class Membership (VDM++ and VDM-RT) . 76 6.20 Class Membership . 77 6.21 Same Base Class Membership (VDM++ and VDM-RT) . 77 6.22 Same Class Membership (VDM++ and VDM-RT) . 78 6.23 History Expressions (VDM++ and VDM-RT) . 78 6.24 The Time Expression (VDM-RT) . 80 6.25 Literals and Names . 80 6.26 The Undefined Expression . 82 6.27 The Precondition Expression . 83 7 Patterns 85 7.1 Object Pattern (VDM++ and VDM-RT) . 90 8 Bindings 93 9 Value (Constant) Definitions 95 10 Declaration of Modifiable State Components 97 10.1 Instance Variables (VDM++ and VDM-RT) . 97 10.2 The State Definition (VDM-SL) . 99 iv CONTENTS 11 Operation Definitions 101 11.1 Constructors (VDM++ and VDM-RT) . 108 12 Statements 109 12.1 Let Statements . 109 12.2 The Define Statement . 111 12.3 The Block Statement . 112 12.4 The Assignment Statement . 113 12.5 Conditional Statements . 117 12.6 For-Loop Statements . 119 12.7 The While-Loop Statement . 121 12.8 The Nondeterministic Statement . 122 12.9 The Call Statement . 124 12.10The Return Statement . 127 12.11Exception Handling Statements . 127 12.12The Error Statement . 130 12.13The Identity Statement . 131 12.14Start and Start List Statements (VDM++ and VDM-RT) . 132 12.15Stop and Stop List Statements (VDM++ and VDM-RT) . 133 12.16The Specification Statement . 134 12.17The Duration Statement (VDM-RT) . 135 12.18The Cycles Statement (VDM-RT) . 137 13 Top-level Specification in VDM 139 13.1 Top-level Specification in VDM-SL . 139 13.1.1 A Flat Specification . 139 13.1.2 A Structured Specification . 141 13.2 Top-level Specification in VDM++ and VDM-RT . 148 13.3 System (VDM-RT) . 148 13.3.1 Classes . 151 13.3.2 Inheritance . 153 13.3.3 Interface and Availability of Class Members . 155 14 Synchronization Constraints (VDM++ and VDM-RT) 161 14.1 Permission Predicates . 162 14.1.1 History guards . 163 14.1.2 The object state guard . 164 14.1.3 Queue condition guards . 165 14.1.4 Evaluation of Guards . 166 14.2 Inheritance of Synchronization Constraints . 166 14.2.1 Mutex constraints . 166 v VDM-10 Language Manual 15 Threads (VDM++ and VDM-RT) 169 15.1 Periodic Thread Definitions (VDM-RT) . 169 15.2 Sporadic Thread Definitions (VDM-RT) . 172 15.3 Procedural Thread Definitions (VDM++ and VDM-RT) . 173 16 Trace Definitions 177 A The Syntax of the VDM Languages 185 A.1 VDM-SL Document . 185 A.1.1 Modules . 185 A.2 VDM++ and VDM-RT Document . 187 A.3 System (VDM-RT) . 187 A.3.1 Classes . 187 A.4 Definitions . 187 A.4.1 Type Definitions . ..